Orthonormal wavelets and shift invariant generalized multiresolution analyses
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- by Sharon Schaffer Vestal and Eric Weber PDF
- Proc. Amer. Math. Soc. 131 (2003), 3089-3100 Request permission
Abstract:
All wavelets can be associated to a multiresolution-like structure, i.e. an increasing sequence of subspaces of $L^2({\mathbb R})$. We consider the interaction of a wavelet and the shift operator in terms of which of the subspaces in this multiresolution-like structure are invariant under the shift operator. This action defines the notion of the shift invariance property of order $n$. In this paper we show that wavelets of all levels of shift invariance exist, first for the classic case of dilation by 2, and then for arbitrary integral dilation factors.References
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Additional Information
- Sharon Schaffer Vestal
- Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80309-0395
- Address at time of publication: Department of Computer Science, Mathematics and Physics, Missouri Western State College, St. Joseph, Missouri 64507
- Email: sharonv@mwsc.edu
- Eric Weber
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
- Address at time of publication: Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071-3036
- MR Author ID: 660323
- Email: weber@math.tamu.edu, esw@uwyo.edu
- Received by editor(s): April 23, 2002
- Published electronically: January 15, 2003
- Communicated by: David R. Larson
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3089-3100
- MSC (2000): Primary 42C40, 46N99
- DOI: https://doi.org/10.1090/S0002-9939-03-06928-4
- MathSciNet review: 1993218